Almost hypoelliptic operators with constant powers

The concept of a formally almost hypoelliptic operator with constant power and the concept of weighted Sobolev spaces generated by such operators are introduced. We prove some properties of such operators, establish some estimates for functions in those spaces, in particular, the density of smooth functions in those spaces. We intend, in another work, using the results of this paper, to select a set of infinitely differentiable solutions for a class of almost hypoelliptic equations having constant power.